用神经网络实现贝叶斯推断的快速估算，一次训练即可应对不同数据和温度参数。
Amortized Simulation-Based Inference in Generalized Bayes via Neural Posterior Estimation
- 训练一个条件神经后验模型，可一次性生成多种温度下的后验分布
- 在4个基准任务中表现媲美传统马尔可夫链采样方法，且速度更快
- 适合需要快速迭代、多温度分析的模拟推断场景
广义贝叶斯推断（GBI）通过引入温度β>0的损失调整来缓解过自信问题并提升模型误设下的鲁棒性。然而现有方法通常依赖昂贵的MCMC或SDE采样器，且每次新数据或β值都需重新运行。本文首次提出对温度化后验族的完全可迁移变分近似：仅需训练一个数据与β条件化的神经后验估计器，即可在单次前向传播中完成采样，无需模拟器调用或推理阶段的MCMC。我们设计两种互补的训练路径：一种从温度化联合分布中合成非流形样本，另一种使用自归一化重要性采样（SNIS）重加权固定基础数据集。我们证明，基于SNIS的损失目标能以有限权重方差一致地拟合前向KL散度。在四个标准模拟推断基准测试中，包括混沌的Lorenz-96系统，该β-可迁移估计器在双样本指标下表现优异，与非可迁移的基于幂后验的MCMC采样器在广泛温度范围内相当。
原文摘要 · Abstract (English)
Generalized Bayesian Inference (GBI) tempers a loss with a temperature $β> 0$ to mitigate overconfidence and improve robustness under model misspecification, but existing GBI methods typically rely on costly MCMC or SDE-based samplers and must be re-run for each new dataset and each $β$ value. We give the first fully amortized variational approximation for the tempered posterior family by training a single data- and $β$-conditioned neural posterior estimator that enables sampling in a single forward pass, without simulator calls or inference-time MCMC. We introduce two complementary training routes: one synthesizes off-manifold samples from the tempered joint distribution, and the other reweights a fixed base dataset using self-normalized importance sampling (SNIS). We show that the SNIS-weighted objective provides a consistent forward-KL fit to the tempered posterior with finite weight variance. Across four standard simulation-based inference benchmarks, including the chaotic Lorenz-96 system, our $β$-amortized estimator achieves competitive posterior approximations, in standard two-sample metrics, matching non-amortized MCMC-based power-posterior samplers over a wide range of temperatures.
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